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Undergraduate Summer School 2014

The Undergraduate Summer School provides opportunities for talented undergraduate students to enhance their interest in mathematics. This program is open to undergraduates at all levels, from first-year students to those who have just completed their undergraduate education. There will be many organized activities, with some specifically targeted at students at the introductory level and others at more advanced students. There will also be time for study groups and individual projects guided by advisors, as well as other activities.

The 24th Annual PCMI Summer Session will be held June 29 – July 19, 2014.

In the last few decades, mathematics has brought significant clarity to a number of questions about the behavior of materials. In particular, methods from the calculus of variations have proven very valuable for studying stable configurations. This course will provide a foundation for understanding these methods, and explore some advances obtained with them.

What is a crystal? Why do liquids flow? Is there a geometry of glass? These questions have challenged scientists in every era, from “natural philosophers” of antiquity to nanoscience researchers today. In this course we will explore the geometry (in dimensions 2, 3, and higher) that lies behind them: polyhedra (space-filling and otherwise), point lattices and tilings (periodic and non-periodic), and packings of spheres, tetrahedra, and more. We will see that, and why, the famous five regular solids are as important today as ever.